Video: Calculating the Percentage Composition of a Binary Compound from Formula Masses

To 1 decimal place, calculate the oxygen content of a water molecule as a percentage of the total mass.

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Video Transcript

To one decimal place, calculate the oxygen content of a water molecule as a percentage of the total mass.

This is a depiction of a water molecule. It has one oxygen atom and two hydrogen atoms and has the formula H₂O. The question is asking us to calculate the percentage of the total mass that corresponds to oxygen in a water molecule. We could take the approach where we calculate the mass of one water molecule, then calculate the mass of one oxygen atom, and then divide one by the other and multiply by 100 percent.

However, let’s take a peek at our periodic table. This is the record for hydrogen. The periodic table does not tell you the mass of one atom of an element. It tells you the mass of one mole. That’s the mass of 6.022 times 10 to the 23 atoms. Remember that 6.022 times 10 to the 23 is Avogadro’s number N A. So, we could take the molar mass of water, divide it by N A to get the mass of a water molecule. Then take the relative atomic mass of oxygen and divide that by N A to get the mass of an oxygen atom. And then plug them in here. But there’s a much easier way.

The percentage mass of oxygen in a water molecule doesn’t change, no matter how many water molecules you have. Whether you have one water molecule or five water molecules, you’ll still have the same percentage by mass of oxygen. Even if you have so many water molecules, you need to count in moles. So instead of calculation mass of one water molecule, we can calculate the mass of one mole of water molecules. Then calculate the mass of one mole of oxygen atoms. Divide one by the other, multiply by 100 percent, and get exactly the same result. So, that’s what I’m going to do.

The first thing we need to do is calculate the molar mass of water. This is equal to two times the molar mass of hydrogen plus the molar mass of oxygen. If you use your periodic table, you can see that the atomic mass of hydrogen is 1.0 and the atomic mass of oxygen is 16.0. This means that the molar mass of water is 18.0 grams per mole. Since we’re calculating the mass of one mole of water molecules, we know that it will weigh 18 grams.

Now we can move on to step two. According to the periodic table, the relative atomic mass of oxygen is 16.0 grams per mole. Therefore, the mass of one mole of oxygen atoms is 16 grams. So, we have the mass of one mole of water molecules and the mass of the oxygen atoms in those water molecules. Now we just need to divide one by the other and multiply by 100 percent to get our answer.

This is equal to 16.0 divided by 18.0 multiplied by 100 percent. This is equal to 0.8 recurring times 100 percent, which is equal to 88.8 recurring percent. The question asks that our answer is given to one decimal place. So, the percentage of oxygen by mass in a molecule of water is equal to 88.9 percent.

This was just one way of doing things. As I mentioned, you could have worked out the mass of the water molecule and the mass of an oxygen atom. But you would’ve needed to do more calculation steps, could’ve made mistakes or could have more rounding errors. This way is the most efficient route to the answer. Although, you may have noticed that we didn’t need to work out the mass of one mole of each substance. We could have used the molar masses straightaway because the units cancel. Either way, this would’ve led to our final answer of 88.9 percent.